I prefer a room sized quality area rug over a finished floor myself, but a good room sized rug usually costs more than carpet, so its not really the most economic route!
Poo and vomit usually clean up eaily, pick it up (I like to cut a paper plate in half and use the two halves to "scoop" it up to avoid grinding it into the carpet), then use an enzyme cleaner or diluted vinegar to clean and they won't stain. Urine is tougher; the problem with dog urine accidents on carpet is they sink through to the pad and sometimes the floors, and if you have wall-to-wall its hard to get to all the mess and get it cleaned. If the dog smells it deep in the fibers (and they can smell way better than us) they might go there again. You need to use an enzyme cleaner that can actually change the chemical composition of urine to clean up urine and use enough that it soaks through to wherever the urine went. If you have a nice finished floor under the carpeting and it gets wet with urine it can get damaged, but a sealed subfloor would be just fine.
Pick a color of carpet that coordinates with your dog so his hair doesn't show real badly (I have dogs that shed white and had a carpet with a black and red design...bad idea - it looked hairy an hour after we vacuumed!), and not too light to avoid stains showing easily.
It helps if you get the right kind of carpet: polypropylene resists moisture and wears better than nylon. You can get a water resistant pad for underneath as well, ask where you buy the carpet. Wool is very sturdy and moisture resistant, but if it gets wet it will sometimes shrink or otherwise get misshapen, so if you do have to clean up a mess then you can't use a regular steam cleaner or soak it with enzyme cleaner - it will need professionally cleaned.
Keep your dog clean and brushed, and keep his feet tidy so he doesn't track in mud, and vacuum regularly and your carpet should be fine.
As far as picking a dog, small dogs *can* be harder to housetrain...probably because they move quicker and have smaller bladders so I think they need to pee more often than bigger dogs. Also, a small Chihuahua or Yorkie sized accident can get hidden and you not see it until later, so the behavior becomes learned...it is much harder to un-learn something than to learn it right in the first place. I have small dogs and big dogs and both were housetrained quickly, but I also was very vigilant and made sure they didn't have access to areas of the house where I couldn't see them. Its natural for a dog to seek a private and absorbent area to pee on...most dogs will go straight for the carpet vs. the hard floor because nature says "pee where it gets soaked up."
Good luck and post pictures of your new baby when you get him or her!